Since May 2023 I work as an Assistant Professor of Operations Research at Tilburg University, Tilburg School of Economics and Management, Department of Econometrics and Operations Research.
I obtained my PhD in mathematics under supervision Lex Schrijver at the University of Amsterdam (September 2019). After my PhD, I have worked as an operations research engineer at ORTEC - Optimize Your World in Zoetermeer (October 2019 - August 2020). After that, I worked as a postdoctoral researcher with Monique Laurent at Centrum Wiskunde en Informatica (CWI) in the research group Networks and Optimization (September 2020 - April 2023).
My PhD-thesis, New methods in coding theory: Error-correcting codes and the Shannon capacity, can be found here and on arXiv:2005.02945 (see this link for general information about the thesis). I also hold a master's degree in Dutch Law (obtained at the University of Amsterdam, 2017).
My research is in the intersection of discrete mathematics and optimization. I am interested in convex relaxations of hard optimization problems and in using algebraic techniques to reduce complexity in combinatorial, polynomial and semidefinite optimization. I am broadly interested in discrete mathematics, including coding theory.
Contact information:
Email: s.c.polak *at* tilburguniversity *dot* edu
Koopmans Building, room K 408
Warandelaan 2
5037 AB Tilburg
Netherlands
Preprints:
- M. Laurent, S.C. Polak, L.F. Vargas, Semidefinite approximations for bicliques and biindependent pairs, arXiv:2302.08886 (2023)
- S.J. Gribling, S.C. Polak, Mutually unbiased bases: polynomial optimization and symmetry, arXiv:2111.05698 (2021)
Accepted:
- D. Brosch, S.C. Polak, New lower bounds on crossing numbers of Km,n from semidefinite programming, arXiv:2206.02755 (2022), accepted for publication in Mathematical Programming
Published:
- S.C. Polak, Symmetry reduction to optimize a graph-based polynomial from queueing theory, SIAM Journal on Applied Algebra and Geometry, 6 (2022), 243-266, SIAM, arXiv:2104.08264
- S. Della Fiore, A. Gnutti, S.C. Polak, The maximum cardinality of trifferent codes of lengths 5 and 6, Examples and Counterexamples, 2 (2022), 100051, ScienceDirect, arXiv:2201.06846
- S.C. Polak, A. Schrijver, New lower bound on the Shannon capacity of C7 from circular graphs, Information Processing Letters, 143 (2019), 37-40, ScienceDirect, arXiv:1808.07438
- S.C. Polak, Semidefinite programming bounds for Lee codes, Discrete Mathematics, 342 (2019), 2579-2589, ScienceDirect, arXiv:1810.05066. Link to computer programs used for this paper.
- A.E. Brouwer, S.C. Polak, Uniqueness of codes using semidefinite programming, Designs, Codes and Cryptography, 87 (2019), 1881-1895, PDF, arXiv:1709.021951. Link to computer programs used for this paper: Google Drive, GitHub
- B.M. Litjens, S.C. Polak, V. Sivaraman, Sum-perfect graphs, Discrete Applied Mathematics, 259 (2019), 232-239, ScienceDirect, arXiv:1710.07546
- S.C. Polak, Semidefinite programming bounds for constant weight codes, IEEE Transactions on Information Theory, 65 (2019), 28-38, IEEE Xplore, PDF, arXiv:1703.05171
- S.C. Polak, New nonbinary code bounds based on divisibility arguments, Designs, Codes and Cryptography, 86 (2018), 861-874, PDF, arXiv:1606.05144
- B.M. Litjens, S.C. Polak, A. Schrijver, Semidefinite bounds for nonbinary codes based on quadruples, Designs, Codes and Cryptography, 84 (2017), 87-100, PDF, arXiv:1602.02531
Conference proceedings:
- S. Gribling, S.C. Polak, L. Slot, A note on the computational complexity of the Moment-SOS hierarchy for polynomial optimization, in International Symposium Symbolic and Algebraic Computation (ISSAC 2023), 280-288, Proceedings
- R. Brokkelkamp, S.C. Polak, G. Schäfer, Y. Velaj, Approximate pricing in networks: how to boost the betweenness and revenue of a node, in 30th International Symposium on Algorithms and Computation (ISAAC 2019), 13:1-13:15, Proceedings
- B.M. Litjens, S.C. Polak, B.L. Sevenster, L. Vena, On the chromatic number of a subgraph of the Kneser graph, Electronic Notes in Discrete Mathematics, 68 (2018), 227-232, Proceedings (new extended version on arXiv: arXiv:1803.04342 (2018))
Some recent and future talks:
-EUROpt, Budapest. 23-25 August 2023, New bounds for crossing numbers of complete bipartite graphs (joint work with Daniel Brosch).
-SIAM Conference on Applied Algebra and Geometry, Eindhoven, July 10-14 2023, On the computational complexity of the moment-SOS Hierarchy (joint work with Sander Gribling and Lucas Slot)
-Workshop Combinatorics in Digital Communication, Eindhoven, 19-21 April 2023, Uniqueness of codes using semidefinite programming (talk partly based on joint work with Andries Brouwer)
-KdVI Discrete Mathematics Seminar, UvA Amsterdam, 1 February 2023, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-TU/e Lunch seminar in Combinatorial Optimization, TU Eindhoven, 14 October 2022, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-International Conference on Continuous Optimization (ICCOPT), Lehigh University, Pennsylvania. 25-28 July 2022, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-POEMA Final workshop, Paris. 5-9 September 2022, New bounds for crossing numbers of complete bipartite graphs (joint work with Daniel Brosch). Youtube recording
-Nordic Combinatorial Conference (NORCOM), Tromsø. 7-9 June 2022, New bounds for crossing numbers from permutation modules and semidefinite programming (joint work with Daniel Brosch)
-International Symposium on Combinatorial Optimization (ISCO), Online. 18-20 May 2022, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-Dutch Day of Combinatorics, Eindhoven, 12 May 2022, New bounds for crossing numbers from permutation modules and semidefinite programming (joint work with Daniel Brosch)
-N&O Seminar, CWI, 2 February 2022, Mutually unbiased bases: polynomial optimization and symmetry (joint work with Sander Gribling)
-BrainPop seminar Toulouse, Online, 24 January 2022, Mutually unbiased bases: polynomial optimization and symmetry (joint work with Sander Gribling)
-SIAM conference on Applied Algebra and Geometry, Online, August 16-20, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-SIAM conference on Optimization, Online, July 20-23, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-Tilburg TiSEM seminars on Operations Research, Online, May 27, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-DIAMANT symposium, Online, April 7, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-University of Amsterdam, Discrete Mathematics Seminar at KdvI, Online, April 1, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-Landelijk Netwerk Mathematische Besliskunde, Conference on the Mathematics of Operations Research, Lunteren, January 16-18, 2018, Uniqueness of codes using semidefinite programming (joint work with Andries Brouwer)
-Workshop on analytic combinatorics, Zámeček, 27-31 March 2017, New upper bounds for nonbinary codes based on a divisibility argument
-Workshop on Algebraic Graph Theory, Pilsen, 3-7 October 2016, Semidefinite bounds for nonbinary codes based on quadruples (joint work with Bart Litjens and Lex Schrijver)
-6th SDP day at CWI, Amsterdam, 30 June 2016, Semidefinite bounds for nonbinary codes based on quadruples (joint work with Bart Litjens and Lex Schrijver)
Teaching (Lectures):
- 2023/2024: Linear Algebra (Tilburg University, Bachelor Econometrics and Operations Research), Essential Mathematics for Data Science (Minor Data Science)
- 2022/2023: Networks and semidefinite programming (LNMB PhD course, with Monique Laurent)
Teaching (Tutorials at the University of Amsterdam):
- 2017/2018: Linear algebra; Functional analysis
- 2016/2017: Algebra 2 (ring and field theory); Galois theory
- 2015/2016: Analysis on the real line; Introductory graph theory
Thesis:
- New methods in coding theory: Error-correcting codes and the Shannon capacity, PhD-thesis under supervision of Lex Schrijver, 2019
- Algorithms for the network analysis of bilateral tax treaties, Master thesis at the CWI/CPB/UvA under supervision of Guido Schaefer, 2014
- Kwadratische Vormen, Bachelor thesis at the UvA (in Dutch) under supervision of Gerard van der Geer, 2012